chapter  6
32 Pages

Statistical Inference

Consider the normal Gauss-Markov model given by y ∼ NN (Xb, σ 2IN ). Under the assumption of normality, we know the distribution of the best linear unbiased estimatorΛT bˆ of an estimableΛTb is N (ΛTb, σ 2ΛT (XTX)gΛ) and it is independent of SSE/σ 2 ∼ χ2N−r . We construct the unbiased estimator for σ 2 as σˆ 2 = SSE/(N−r) fromSection 4.3.Beyond this point,we seek to establish somebasic inferential results. First, we wish to find further properties of the usual estimators relying now on the normality assumption. The construction of hypothesis tests requires a few steps of its own: a test based on first principles, then the likelihood ratio test, and unifying the two while examining the effect of constraints. Construction of confidence intervals leads to the usual results on multiple comparisons.